BUDDHACARITA 12.52: The Second Dhyāna, By the Book

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jñātvā vidvān vitarkāṁs-tu manaḥ-saṁkṣobha-kārakān |

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tad-viyuktam-avāpnoti dhyānaṁ prīti-sukhānvitam || 12.52

12.52

The wise one, in contrast, knowing thoughts

To cause agitation of the mind,

Arrives at a stage divorced from that,

A dhyāna containing its own joy and ease.

COMMENT:
The passage quoted in the comment on BC12.49, in connection with the first dhyāna, from Mahāsatipaṭṭhānasuttaṁ (DN 22), The Long Discourse about the Ways of Attending to Mindfulness, continues as follows: 

Vitakkavicārānaṁ vūpasamā 

With the calming down of thinking and reflection,

ajjhattaṁ sampasādanaṁ, cetaso ekodibhāvaṁ,
[he realizes the stage of] internal clarity, and one-pointedness of mind,

avitakkaṁ, avicāraṁ, samādhijaṁ pītisukhaṁ, 
which is without thinking, without reflection, 
having the joy and ease born of balanced stillness --

dutiyaṁ jhānaṁ upasampajja viharati.
he dwells having attained the second dhyāna.

(This is Ānandajoti Bhikkhu's text and translation, somewhat revised for conformity.)

Hence, going by the book, the second dhyāna is always characterized by 

pītisukhaṁ (DN 22), joy and ease 

prīti-sukha (SN17.47), joy and ease 

prīti-sukha (BC12.52), joy and ease

Other translations of prīti-sukha are available, but for the present I am staying with joy and ease. 

Together with the joy and ease, the second dhyāna is characterized by a unitary awareness, or one-pointedness of the mind, in which disturbing thoughts have been left behind. Hence, 

ajjhattaṁ sampasādanaṁ, cetaso ekodibhāvaṁ (DN 22),  internal clarity, and one-pointedness of mind 

ekāgra-bhāvān manasaḥ prasannam (SN17.47), the mind tranquil from one-pointedness

In today's verse, the one-pointedness is understood, not specified, but the common gist is evident: that the thoughts which are allowed to makes waves in the first dhyāna are not allowed to make waves in the second dhyāna. Hence, going back to a slightly reworked version of the relevant verses in SN Canto 17 (taking vitarka as thought and vicāra as reflection): 

kāmair viviktaṃ malinaiś ca dharmair vitarkavac cāpi vicāravac ca /
Secluded from desires and tainted things, containing thoughts and reflections,
viveka-jaṃ prīti-sukhopapannaṃ dhyānaṃ tataḥ sa prathamaṃ prapede //SN17.42 
Born of seclusion and possessed of joy and ease, 

is the first stage of meditation, which he then entered.

kāmāgni-dāhena sa vipramukto hlādaṃ paraṃ dhyāna-sukhād avāpa /
Released from the burning of the bonfire of desires, 

he derived great gladness from ease in the act of meditating --
sukhaṃ vigāhyāpsv iva gharma-khinnaḥ prāpyeva cārthaṁ vipulaṃ daridraḥ //17.43 
Ease like a heat-exhausted man diving into water. 

Or like a pauper coming into great wealth.

tatrāpi tad-dharma-gatān vitarkān guṇāguṇe ca prasṛtān vicārān /
Even in that, he realised, thoughts about aforesaid things, 

and reflections on what is or is not good,
buddhvā manaḥ-kṣobha-karān aśāntāṃs tad-viprayogāya matiṃ cakāra // 17.44 
Are something not quieted, causing disturbance in the mind, 

and so he decided to cut them out.

kṣobhaṃ prakurvanti yathormayo hi dhīra-prasannāmbu-vahasya sindhoḥ /
For, just as waves produce disturbance 
in a river bearing a steady flow of tranquil water,

ekāgra-bhūtasya tathormi-bhūtāś cittāmbhasaḥ kṣobha-karā vitarkāḥ // 17.45 
So thoughts, like waves, disturb the water of the one-pointed mind.

khinnasya suptasya ca nirvṛtasya bādhaṃ yathā saṃjanayanti śabdāḥ /
And just as noises are a source of bother to one who is weary, and fallen fast asleep,
adyātmam-aikāgryam upāgatasya bhavanti bādhāya tathā vitarkāḥ // 17.46 
So do thoughts become bothersome 

to one indulging in the original state of unitary awareness.

athāvitarkaṃ kramaśo 'vicāram-ekāgra-bhāvān manasaḥ prasannam /
And so gradually bereft of thought and reflection, 

his mind tranquil from one-pointedness,
samādhi-jaṃ prīti-sukhaṃ dvitīyaṃ dhyānaṃ tad-ādhyātma-śivaṃ sa dadhyau //SN17.47
He realised the joy and ease born of balanced stillness 

-- that inner happiness which is the second dhyāna.

VOCABULARY

jñātvā = abs. jñā: to know

vidvān (nom. sg. m.): the wise one

vitarkān (acc. pl.): m. thoughts, ideas

tu: but

manaḥ-saṁkṣobha-kārakān (acc. pl. m.): causing agitation of the mind

tad-viyuktam (acc. sg. n.): disjoined from all that, exempt from such agitation

viyukta: mfn. disjoined , detached , separated or delivered from , deprived or destitute of, deserted by (instr. or comp.)

avāpnoti = 3^rd pers. sg. ava√āp: to reach , attain , obtain , gain , get

dhyānam (acc. sg.): n. thinking, meditation, Zen

prīti-sukhānvitam (acc. sg. n.): possessed of its own gladness and

prīti: f. any pleasurable sensation , pleasure , joy , gladness , satisfaction

sukha: n. n. ease , easiness , comfort , prosperity , pleasure , happiness

anvita: mfn. gone along with ; having as an essential or inherent part , endowed with , possessed of , possessing

慧者能自知 方便止覺觀
精勤求上進 第二禪相應